Eur. Phys. J. D 52, 159-162 (2009)
https://doi.org/10.1140/epjd/e2009-00009-9

Exact diagonalization of Hubbard clusters at finite temperatures

¹ Advanced Materials Department, IPICYT, 78216 San Luis Potosí, Mexico
² Institut für Theoretische Physik, Universität Kassel, 34132 Kassel, Germany

Corresponding author: ^a pastor@uni-kassel.de

Received: 19 September 2008
Published online: 24 January 2009

Abstract

Finite temperature electronic and magnetic properties of small clusters are investigated in the framework of the Hubbard model by using exact diagonalization methods and by sampling the different cluster topologies exhaustively. Results are discussed for the specific heat C(T), magnetic susceptibility χ(T), local magnetic moments μ_i(T), average magnetic moments and spin-correlation functions γ_ij(T). Representative cluster sizes and band-fillings are considered showing antiferromagnetic-like (AF) and ferromagnetic-like (FM) behaviors. For half-band filling ν= N the susceptibility shows an AF high-temperature behavior of the form χ≈1/(T + T_N) from which the cluster `Néel' temperature T<sub>N</sub> is derived. In contrast, for ν= N + 1 a FM high-temperature behavior of the form χ≈1/(T - T<sub>C</sub>) is found, where T<sub>C</sub> can be interpreted as the cluster `Curie' temperature. In both cases one also observes peaks in C(T), either at T≃T_N or T≃T_C, which reflect the development of spin fluctuations and the breakdown of the low-temperature short-range magnetic order. The dependence of T_N and T_C on cluster size N and interaction strength U/t is analyzed in terms of effective Heisenberg spin interactions. Finally, the effects of temperature-induced structural fluctuations are discussed.